Apply color ramp to a face?
You're using cycles so you'll need a node setup, similar to this



where you see that there are two materials. The "gradient" one is "assigned" to the single face, while all the rest uses the default grey one.

The material needs a factor that rules the Colorramp transition, provided by a Gradient Texture, which needs the coordinates to be mapped to that face only: for this you need a UVmap: in edit mode select only the face, press U and select "unwrap". Done.